There's a handful of ways to address how two pilot stations could control a craft, each having their pros and cons.
Boeing uses mechanical linkages between the controls on both control yokes, If there is a dispute on who is in control then I guess the stronger pilot wins. This makes the control yoke as much of an indicator as a control. It shows to the pilot monitoring what the pilot flying is inputing to the control surfaces. When the autopilot is active the yoke moves to indicate to the crew what the computer is doing.
AirBus control sticks are not mechanically linked and the fly by wire system averages the inputs. I found this interesting in the discussion of an AirBus crash. In an attempt to recover from a stall one pilot decided they needed speed and so was pushing the control stick full ahead, this would trade altitude for speed. The other pilot (as I recall having less experience than the other) wanted to gain altitude and so was pulling the control stick full back, this would reduce the speed of the craft as it climbs. The fly by wire system averaged the inputs and centered the elevator position. The plane crashed. I believe that AirBus aircraft have the ability to lock out one or both stations from controlling the aircraft, this to prevent an accidental bump from a crew member climbing into their seat and giving the aircraft a bump as well. Locking out both pilot stations would obviously mean the autopilot is in control.
I recall seeing some commentary on a US Navy ship collision where either of the two pilot stations can be selected. This "fly by wire" ship can also divide duties between the stations, an example being one pilot controlling the rudder and the other the engine throttles. One contributing factor of the collision was that there was confusion on which pilot was controlling what. As an aside there was confusion on who was giving orders as the captain came to the bridge but had not stated explicitly that he was giving orders to the crew or acting as an observer and giving suggestions to the conning officer. It might seem obvious that the captain's orders always supersede that of a subordinate but that's not always the case. Why this is the case gets into hundreds of years of maritime traditions.
Seeing a clip from GotG2 implies the pilot station in control of the ship is selected. As the two fought over control of the ship there were green lights that would light up next to Quill and Rocket indicating who was flying at the time. I don't recall what lever, button, or whatever it was that selected the active pilot station, only that the station which was controlling the craft alternated between the two.